Mathematics
Intermediate
50 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen

Perimeter of Rectangles and Simple Shapes

Learn to find the perimeter of rectangles by using their equal opposite sides. Work out missing measurements, then add all the way around to find the total distance.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedLook at this rectangle. The top is labelled 6 cm and one side is labelled 3 cm. The other two sides have no numbers on them yet.

    What must those two sides be? And how can you be so sure without measuring them?

    2 - Watch and Notice ~8 mins

    A 6 cm by 3 cm rectangle

    Watch as we add the sides all the way around: 6 + 3 + 6 + 3. The two long sides match and the two short sides match, so the perimeter is 18 cm.

    A 5 cm square

    A square is a special rectangle where every side is the same. Watch four lots of 5 added together to make the way around.

    A 7 cm by 2 cm rectangle

    This long thin one still has two pairs of matching sides. Watch us fill the missing sides in first, then add.

    3 - Try It Together ~11 mins

    Let's work through some rectangles together. I'll set the two sides each time, and you fill in the matching opposite sides and read off the perimeter. Each time, check that the two opposite sides really do match before you add.

    Find the missing sides, then the perimeter

    4 - Draw the Rectangle in Your Copy ~5 mins

    COPYBOOK MOMENT

    In your maths copy, draw a 5 cm by 3 cm rectangle. Write the length on all four sides, then write the perimeter sentence with its total underneath.

    5 - Class Challenge ~11 mins

    Let's work through these shapes together, one picture at a time on the board: a 4 cm by 4 cm square, a 6 cm by 3 cm rectangle, a 7 cm by 4 cm rectangle, and an L-shape made from two rectangles. For each shape we look at, find the hidden sides first, then add all the way around.

    Find the perimeter of each of these shapes by filling in any missing sides first, then adding all the way around.

    1. Perimeter of a 4 cm by 4 cm square.
    2. Perimeter of a 6 cm by 3 cm rectangle.
    3. Perimeter of a 7 cm by 4 cm rectangle.
    4. Perimeter of an L-shape that is 6 cm along the bottom and 4 cm up the left side, with a 2 cm by 2 cm square notch cut out of the top-right corner. Going around it, the six sides are 6 cm (bottom), 4 cm (left), 2 cm (top-left part), 2 cm (down into the notch), 4 cm (across the notch) and 2 cm (up to the start).

    Ways to start:

    • Start by writing the length on every side, copying matching opposite sides where a number is missing.
    • Touch each side once as you add it, so no side is counted twice.

    Stretch:

    • For the L-shape, work out the hidden sides from the sides you can see before you add.
    Answers & strategies (teacher)
    1. Perimeter of a 4 cm by 4 cm square. — 16 cm
    2. Perimeter of a 6 cm by 3 cm rectangle. — 18 cm
    3. Perimeter of a 7 cm by 4 cm rectangle. — 22 cm
    4. Perimeter of an L-shape that is 6 cm along the bottom and 4 cm up the left side, with a 2 cm by 2 cm square notch cut out of the top-right corner. Going around it, the six sides are 6 cm (bottom), 4 cm (left), 2 cm (top-left part), 2 cm (down into the notch), 4 cm (across the notch) and 2 cm (up to the start). — 20 cm
    • Square 4 cm: 4 + 4 + 4 + 4 = 16 cm.
    • Rectangle 6 cm by 3 cm: 6 + 3 + 6 + 3 = 18 cm.
    • Rectangle 7 cm by 4 cm: 7 + 4 + 7 + 4 = 22 cm.
    • L-shape: 6 + 4 + 2 + 2 + 4 + 2 = 20 cm, finding any hidden side from the others first.

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    If you know the long side and the short side of a rectangle, why don't you need to measure the other two sides at all?

    7 - What's Next ~3 mins

    What we learned

    • A rectangle has two pairs of equal sides, so two measurements tell you all four.
    • To find the perimeter, fill in any missing sides first, then add every side once.

    Coming up

    Coming up

    Next we move from the way around a shape to the space inside it, counting square units to find area.

    Pupil practice
    Module 5 · Area, Perimeter and Volume Measures
    Lesson 54 · Perimeter of Rectangles and Simple Shapes
    Download Activity Book page (PDF)
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